As anticipated above, the framework that we shall use to derive and analyze the methods is that of the so called line integral methods, namely methods where the conservation properties are derived by the vanishing of a corresponding line integral [1]}, [2]}. Such methods have been largely investigated in the case of Hamiltonian problems, providing their major instance given by Hamiltonian Boundary Value Methods (HBVMs). The analysis will strictly follow that in [3]} and [4]}. To begin with, let us consider problem (REF ) on the interval \([0,h]\) ,
\(\dot{y}(ch) = B(y(ch)) \nabla H(y(ch)),\qquad c\in [0,1], \qquad y(0) = y_0.\) 
